Scaling method for the pair-density-functional theory in combination with energy functionals satisfying the virial theorem: Checking the validity via atomic-structure calculations

We perform atomic-structure calculations for the neutral Ne, Mg, and Ar atoms on the basis of the recently proposed correction method (scaling method) for the pair-density (PD) -functional theory [Phys. Rev. A 84, 044502 (2011)]. The formal features of the scaling method are that the search region of PDs is substantially extended and that the resultant variationally best PD, which can be obtained without the heavy calculation tasks, satisfies the virial theorem rigorously. To enjoy the benefit of these features, we also develop the approximate form of the kinetic energy functional. It is shown by the atomic-structure calculations that the scaling method can improve well not only various energy functionals but also the spatial profiles of the electron density and exchange-correlation hole. Especially it is found that the scaling method makes preferential modifications to the energetically effective regions of the electron density and exchange-correlation hole. These results suggest that the scaling method efficiently puts the PD close to the correct ground-state PD. DOI: 10.1103/PhysRevA.87.03251